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In this paper, we will apply cubic B-splines on a uniform mesh to explore the numerical solutions and numerical derivatives of a class of nonlinear second-order boundary value problems with two dependent variables. Our new method is based on the cubic spline interpolation. The analytical solutions and any-order derivatives can be well approximated with 4th order accuracy. Furthermore, our new method is also able to solve general nonlinear 4th-order two-point boundary value problems. Numerical results show that our method is very practical and effective. a0(x)u 00 +a1(x)u 0 +a2(x)u +a3(x)v 00 +a4(x)v 0 +a5(x)v +G1(x;u;v) = f1(x); b0(x)v 00 +b1(x)v 0 +b2(x)v +b3(x)u 00 +b4(x)u 0 +b5(x)u +G2(x;u;v) = f2(x);

A new cubic B-spline method for approximating the solution of a class of nonlinear second-order boundary value problem with two dependent variables